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Production of energy is a foundation of life. The metabolic rate of organisms (amount of energy produced per unit time) generally increases slower than organisms’ mass, which has important implications for life organization. This phenomenon, when considered across different taxa, is called interspecific allometric scaling. Its origin has puzzled scientists for many decades, and still is considered unknown. In this paper, we posit that natural selection, as determined by evolutionary pressures, leads to distribution of resources, and accordingly energy, within a food chain, which is optimal from the perspective of stability of the food chain, when each species has sufficient amount of resources for continuous reproduction, but not too much to jeopardize existence of other species. Metabolic allometric scaling (MAS) is then a quantitative representation of this optimal distribution. Taking locomotion and the primary mechanism for distribution of energy, we developed a biomechanical model to find energy expenditures, considering limb length, skeleton mass and speed. Using the interspecific allometric exponents for these three measures and substituting them into the locomotion-derived model for energy expenditure, we calculated allometric exponents for mammals, reptiles, fish, and birds, and compared these values with allometric exponents derived from experimental observations. The calculated allometric exponents were nearly identical to experimentally observed exponents for mammals, and very close for fish, reptiles and the basal metabolic rate (BMR) of birds. The main result of the study is that the MAS is a function of a mechanism of optimal energy distribution between the species of a food chain. This optimized sharing of common resources provides stability of a food chain for a given habitat and is guided by evolutionary pressures and natural selection.

In this study, the development of a graphite paste electrode (GPE) modified by copper oxide nanoparticles (CuO@GP) to be used as a practical and economical sensor for the electrochemical sensing of malachite green (MG) has been elucidated. The sol–gel technique was applied for the synthesis of CuO nanoparticles (NPS) from copper chloride (CuCl${}_2)$, where the surfactant cetylpyridinium chloride (C${}_{21}$H${}_{38}$NCl) played the role of a capping agent. The synthesized CuO NPS were characterized by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS) and scanning electron microscopy (SEM). A bare GPE was modified using these CuO NPS and thus developed; the new electrode was used as a working electrode (WE) in a 3-electrode system for studying the cyclic voltammetry (CV) and differential pulse voltammetry (DPV) responses of MG. Phosphate buffered saline (PBS) with a pH value of 6 was used as the optimum buffer. Using DPV, a widely linear operational range of 1–1000 $\mu$M was obtained with a detection limit of 0.18 $\mu$M. This CuO@GP provided excellent repeatability, reproducibility and prolonged stability for the MG molecule. For the selectivity study, various common interfering agents were used to observe MG’s corresponding peak current variation. Moreover, this electrode demonstrated a successful application for detecting MG in pond water and fish flesh. This method is effective for similar other applications.